What is the simplest way to generate a dodecahedron?
Go to User Preferences and Navigate to Add Mesh, install the Regular Solids addon and close the preferences window. Now if you hit Shift + A you should see a new menu.



UPDATE

In newer versions of blender (2.75 and up) the Regular Solids addon has been merged with the Extra Objects addon.



To create a dodecahedron go use Shift + A to Add Mesh > Math Function > Regular Solid.



Then on the toolshelf you can select Dodecahedron.